I'd forgotten when I submitted the DT version that there's another verse, which I came across in Howe's Comic Songster (Boston, around 1870). I omit the burden, "Sing song, Kitty, can't you ki' me, oh?"
De wedder's warm, and so am I
I'm sure you'd lub me if you'd try
Your jet-black face I lub to see
Then put on your tucker and be off wid me
(Keemo! Kimo! &c.)
-- I apologise for the political incorrectness of this, but they evidently thought 100 years ago that 'negro dialect' was awfully amusing. If you want a footnote on the "Frog & Mouse/Frog Went a-Courtin" connection, let me know.
A guid New Year when it comes Murray